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On a class of weighted Sobolev spaces and the minimization of quadratic forms

Published online by Cambridge University Press:  14 November 2011

Frans Penning  and
Niko Sauer
Frans Penning
Affiliation:
Department of Mathematics
Niko Sauer
Affiliation:
Department of Applied Mathematics, University of Pretoria, South Africa
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Synopsis

In this paper a class of weighted Sobolev spaces defined in terms of square integrability of the gradient multiplied by a weight function, is studied. The domain of integration is either the space Rn or a half-space of Rn. Conditions on the weight functions that will ensure density of classes of smooth functions or functions with compact support, and compact embedding theorems, are derived. Finally the results are applied to a class of isoperimetrical problems in the calculus of variations in which the domain of integration is unbounded.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 81 , Issue 1-2 , 1978 , pp. 119 - 130
Copyright
Copyright © Royal Society of Edinburgh 1978

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